The negative values can arise due to two major reasons: You did not mention that whether you are using a single beam instrument or a double beam instrument.
In a double beam instrument, absorbance of the sample and the blank is continuously measured. In a single beam spectrophotometer, A(blank) is recorded first and later subtracted. In each case, the output value at each wavelength is:
Abs (measured) = A(sample)- A (blank)
If at any region of the spectrum A(blank) is larger you get slightly negative absorbance values. This could be due to several reasons including refractive index differences. Under ideal cases, the cuvet which contains the blank is same as cuvet containing the sample or both of them should be optically matched i.e. they should show identical absorbance readings at given wavelengths.
Another reason to see random negative values is that noise is a part of any instrumental analysis. Eliminating all sources of noises, you still get stuck with shot noise, which originates due to statistical counting of photons. That is the very nature of detection especially in spectroscopic measurements- perhaps the ultimate limit in analytical sciences.